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Efficient Real Space Solution of the Kohn-Sham Equations with Multiscale Techniques
We present a multigrid algorithm for self consistent solution of the
Kohn-Sham equations in real space. The entire problem is discretized on a real
space mesh with a high order finite difference representation. The resulting
self consistent equations are solved on a heirarchy of grids of increasing
resolution with a nonlinear Full Approximation Scheme, Full Multigrid
algorithm. The self consistency is effected by updates of the Poisson equation
and the exchange correlation potential at the end of each eigenfunction
correction cycle. The algorithm leads to highly efficient solution of the
equations, whereby the ground state electron distribution is obtained in only
two or three self consistency iterations on the finest scale.Comment: 13 pages, 2 figure
Quasi-Chemical and Structural Analysis of Polarizable Anion Hydration
Quasi-chemical theory is utilized to analyze the roles of solute polarization
and size in determining the structure and thermodynamics of bulk anion
hydration for the Hofmeister series Cl, Br, and I. Excellent
agreement with experiment is obtained for whole salt hydration free energies
using the polarizable AMOEBA force field. The quasi-chemical approach exactly
partitions the solvation free energy into inner-shell, outer-shell packing, and
outer-shell long-ranged contributions by means of a hard-sphere condition.
Small conditioning radii, even well inside the first maximum of the
ion-water(oxygen) radial distribution function, result in Gaussian behavior for
the long-ranged contribution that dominates the ion hydration free energy. The
spatial partitioning allows for a mean-field treatment of the long-ranged
contribution, leading to a natural division into first-order electrostatic,
induction, and van der Waals terms. The induction piece exhibits the strongest
ion polarizability dependence, while the larger-magnitude first-order
electrostatic piece yields an opposing but weaker polarizability dependence. In
addition, a structural analysis is performed to examine the solvation
anisotropy around the anions. As opposed to the hydration free energies, the
solvation anisotropy depends more on ion polarizability than on ion size:
increased polarizability leads to increased anisotropy. The water dipole
moments near the ion are similar in magnitude to bulk water, while the ion
dipole moments are found to be significantly larger than those observed in
quantum mechanical studies. Possible impacts of the observed over-polarization
of the ions on simulated anion surface segregation are discussed.Comment: slight revision, in press at J. Chem. Phy
Equilibration between Translational and Rotational Modes in Molecular Dynamics Simulations of Rigid Water Requires a Smaller Integration Time-Step Than Often Used
In simulations of aqueous systems it is common to freeze the bond vibration
and angle bending modes in water to allow for a longer time-step for
integrating the equations of motion. Thus fs is often used in
simulating rigid models of water. We simulate the SPC/E model of water using
from 0.5 fs to 3.0 fs. We find that for all but fs,
equipartition between translational and rotational modes is violated: the
rotational modes are at a lower temperature than the translation modes. The
autocorrelation of the velocities corresponding to the respective modes shows
that the rotational relaxation occurs at a time-scale comparable to vibrational
periods, invalidating the original assumption for freezing vibrations. also influences thermodynamic properties: the mean system potential energies
are not converged until fs, and the excess entropy of
hydration of a soft, repulsive cavity is also sensitive to
Application of A Distributed Nucleus Approximation In Grid Based Minimization of the Kohn-Sham Energy Functional
In the distributed nucleus approximation we represent the singular nucleus as
smeared over a smallportion of a Cartesian grid. Delocalizing the nucleus
allows us to solve the Poisson equation for theoverall electrostatic potential
using a linear scaling multigrid algorithm.This work is done in the context of
minimizing the Kohn-Sham energy functionaldirectly in real space with a
multiscale approach. The efficacy of the approximation is illustrated
bylocating the ground state density of simple one electron atoms and
moleculesand more complicated multiorbital systems.Comment: Submitted to JCP (July 1, 1995 Issue), latex, 27pages, 2figure
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